Normal-based methods for a gamma distribution

Details

• Personal Author:
  Krishnamoorthy K ; Mathew T ; Mukherjee S
• Description:
  In this article we propose inferential procedures for a gamma distribution using the Wilson-Hilferty (WH) normal approximation. Specifically, using the result that the cube root of a gamma random variable is approximately normally distributed, we propose normal-based approaches for a gamma distribution for (a) constructing prediction limits, one-sided tolerance limits, and tolerance intervals; (b) for obtaining upper prediction limits for at least l of m observations from a gamma distribution at each of r locations; and (c) assessing the reliability of a stress-strength model involving two independent gamma random variables. For each problem, a normal-based approximate procedure is outlined, and its applicability and validity for a gamma distribution are studied using Monte Carlo simulation. Our investigation shows that the approximate procedures are very satisfactory for all of these problems. For each problem considered, the results are illustrated using practical examples. Our overall conclusion is that the WH normal approximation provides a simple, easy-to-use unified approach for addressing various problems for the gamma distribution. [Description provided by NIOSH]
• Subjects:
  Coal Coal Mining Engineering Geology Mining Occupational Health Safety Software
• Keywords:
  Author Keywords: Confidence Limits Coverage Probability Industrial-hygiene Mathematical-models Models Monitoring-systems Monitors Quantile Samplers Sampling Statistical-analysis Survival Probability Tolerance Limits Wilson-Hilferty Approximation

  More +
• ISSN:
  0040-1706
• Document Type:
  Text
• Funding:
  Grant
• Genre:
  Journal Article
• Place as Subject:
  Louisiana ; Maryland ; OSHA Region 3 ; OSHA Region 6
• CIO:
  National Institute for Occupational Safety and Health (NIOSH)
• Topic:
  Workplace Safety & Health
• Location:
  North America
• Pages in Document:
  69-78
• Volume:
  50
• Issue:
  1
• NIOSHTIC Number:
  nn:20044431
• Citation:
  Technometrics 2008 Feb; 50(1):69-78
• Contact Point Address:
  K. Krishnamoorthy, Department of Mathematics, University of Louisiana at Lafayette, Lafayette, LA 70508
• Email:
  krishna@louisiana.edu
• Federal Fiscal Year:
  2008
• Performing Organization:
  University of Maryland, Baltimore
• Peer Reviewed:
  True
• Start Date:
  20000501
• Source Full Name:
  Technometrics
• End Date:
  20150831
• Collection(s):
  National Institute for Occupational Safety and Health
• Main Document Checksum:
  urn:sha-512:4515701ed89d896dba5048ead6663c1e0e644d5bc541f54c9e4729c2338bf5379d0d49cda2dfc87a85f57941f8224ec110848902d3975c1b25f10a1534625282
• Download URL:
  https://stacks.cdc.gov/view/cdc/200133/cdc_200133_DS1.pdf
• File Type:
  [PDF - 206.67 KB ]